Algebra Examples

$8 (\frac{1}{2} x - \frac{1}{4}) > 12 - 2 x$

Step 1

Simplify $8 (\frac{1}{2} x - \frac{1}{4})$ .

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Step 1.1

Rewrite.

$0 + 0 + 8 (\frac{1}{2} x - \frac{1}{4}) > 12 - 2 x$

Step 1.2

Simplify by adding zeros.

$8 (\frac{1}{2} x - \frac{1}{4}) > 12 - 2 x$

Step 1.3

Combine $\frac{1}{2}$ and $x$ .

$8 (\frac{x}{2} - \frac{1}{4}) > 12 - 2 x$

Step 1.4

Apply the distributive property.

$8 \frac{x}{2} + 8 (- \frac{1}{4}) > 12 - 2 x$

Step 1.5

Cancel the common factor of $2$ .

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Step 1.5.1

Factor $2$ out of $8$ .

$2 (4) \frac{x}{2} + 8 (- \frac{1}{4}) > 12 - 2 x$

Step 1.5.2

Cancel the common factor.

$2 \cdot 4 \frac{x}{2} + 8 (- \frac{1}{4}) > 12 - 2 x$

Step 1.5.3

Rewrite the expression.

$4 x + 8 (- \frac{1}{4}) > 12 - 2 x$

Step 1.6

Cancel the common factor of $4$ .

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Step 1.6.1

Move the leading negative in $- \frac{1}{4}$ into the numerator.

$4 x + 8 (\frac{- 1}{4}) > 12 - 2 x$

Step 1.6.2

Factor $4$ out of $8$ .

$4 x + 4 (2) \frac{- 1}{4} > 12 - 2 x$

Step 1.6.3

Cancel the common factor.

$4 x + 4 \cdot 2 \frac{- 1}{4} > 12 - 2 x$

Step 1.6.4

Rewrite the expression.

$4 x + 2 \cdot - 1 > 12 - 2 x$

Step 1.7

Multiply $2$ by $- 1$ .

$4 x - 2 > 12 - 2 x$

Step 2

Move all terms containing $x$ to the left side of the inequality.

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Step 2.1

Add $2 x$ to both sides of the inequality.

$4 x - 2 + 2 x > 12$

Step 2.2

Add $4 x$ and $2 x$ .

$6 x - 2 > 12$

Step 3

Move all terms not containing $x$ to the right side of the inequality.

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Step 3.1

Add $2$ to both sides of the inequality.

$6 x > 12 + 2$

Step 3.2

Add $12$ and $2$ .

$6 x > 14$

Step 4

Divide each term in $6 x > 14$ by $6$ and simplify.

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Step 4.1

Divide each term in $6 x > 14$ by $6$ .

$\frac{6 x}{6} > \frac{14}{6}$

Step 4.2

Simplify the left side.

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Step 4.2.1

Cancel the common factor of $6$ .

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Step 4.2.1.1

Cancel the common factor.

$\frac{6 x}{6} > \frac{14}{6}$

Step 4.2.1.2

Divide $x$ by $1$ .

$x > \frac{14}{6}$

Step 4.3

Simplify the right side.

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Step 4.3.1

Cancel the common factor of $14$ and $6$ .

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Step 4.3.1.1

Factor $2$ out of $14$ .

$x > \frac{2 (7)}{6}$

Step 4.3.1.2

Cancel the common factors.

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Step 4.3.1.2.1

Factor $2$ out of $6$ .

$x > \frac{2 \cdot 7}{2 \cdot 3}$

Step 4.3.1.2.2

Cancel the common factor.

$x > \frac{2 \cdot 7}{2 \cdot 3}$

Step 4.3.1.2.3

Rewrite the expression.

$x > \frac{7}{3}$

Step 5

The result can be shown in multiple forms.

Inequality Form:

$x > \frac{7}{3}$

Interval Notation:

$(\frac{7}{3}, \infty)$